You make a point about the redundancy in that particular use case, but:
1) w3.org's specifications for HTML 5 http://www.w3.org/TR/html5/document-metadata#the-base-element and HTML 4.01 http://www.w3.org/TR/html401/struct/links.html#h-12.4 use full URLs in the examples, so currently I see an inconsistency. https://html.spec.whatwg.org/multipage/semantics.html#the-base-element uses full URLs too.
2) Suggesting to use a full URL (not necessarily to the current page) prevents the bugs reported in the stackoverflow discussion I linked in the OP; suggesting to use a directory URL has no advantage OTOH.
3) Having a base tag pointing to the current URL can be useful if a single document is saved locally, since all its relative links will still correctly point to the original domain. Also, always using a base tag could be a way to ensure crawling bots use the right URL for relative links.